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A164003
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Decimal expansion of exp(-Pi^2/2).
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0
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0, 0, 7, 1, 9, 1, 8, 8, 3, 3, 5, 5, 8, 2, 6, 3, 6, 5, 6, 0, 7, 8, 0, 1, 3, 6, 6, 3, 9, 6, 3, 7, 1, 2, 0, 2, 9, 5, 5, 3, 6, 2, 3, 1, 8, 0, 8, 1, 5, 9, 7, 9, 4, 7, 5, 5, 8, 0, 3, 7, 1, 8, 1, 2, 4, 1, 2, 1, 3, 1, 8, 8, 6, 9, 7, 5, 6, 6, 5, 0, 8, 9, 5, 9, 6, 1, 0, 7, 9, 4, 3, 9, 8, 6, 5, 6, 6, 2, 3, 3, 0
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Arises in connection with the expansion (e i)^(pi i) = e^(pi i) * i^(pi i) = -1 * exp(pi i log i) = -exp(pi i * pi/2 i) = -exp(-pi^2/2) = -0.00719188335582636560780136639...
One has to be careful about branches of multivalued complex functions. By definition (e i)^(pi i) is exp(pi i log(e i)) [using any of the branches of log] = exp(pi i (1 + pi i/2 + 2 n pi i)) [ for any integer n ] = - exp(- pi^2/2 - 2 n pi^2). There is no imaginary part in any of its branches. If n=0 we get (-1) times the present constant.
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EXAMPLE
| .0071918833558263656078013663963712029553623180815979475580371...
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MATHEMATICA
| Join[{0, 0}, RealDigits[Exp[-Pi^2/2], 10, 120][[1]]] (* From Harvey P. Dale, Jul 11 2011 *)
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CROSSREFS
| Sequence in context: A111293 A019661 A200130 * A069609 A019855 A200288
Adjacent sequences: A164000 A164001 A164002 * A164004 A164005 A164006
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KEYWORD
| nonn,cons
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 06 2010, based on postings to the Sequence Fans Mailing List by Alonso Del Arte, Charles R Greathouse IV, Sean A. Irvine, Robert Israel and other correspondents.
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